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Консультация № 177521
28.03.2010, 23:16
0.00 руб.
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С какой скоростью и в каком направлении должен двигаться эллипс,одна из главных осей которого на 20% короче другой,чтобы для наблюдателя из лабораторной системы отсчета он превратился в круг?
Обсуждение
29.03.2010, 10:54
общий
это ответ
Здравствуйте, Aptemis.
Очевидно, что для того чтобы эллипс превратился в круг необходимо равенство его главных осей. Речь идет о релятивистском сокращении длины стержня:
l=l0[$8730$](1-(v/c)^2),
где l0 - длина в системе наблюдателя, l - длина в движущейся системе, v-скорость движущейся системы, с - скорость света в вакууме
Тогда становится очевидно, что для того чтобы получился круг эллипс должен двигаться вдоль большей из главных осей.
Тогда получаем:
0,8*l0=l0[$8730$](1-(v/c)^2)
0,8=[$8730$](1-(v/c)^2)
0,64=1-(v/c)^2
(v/c)^2=0,36
v/c=0,6
v=0,6c
Ответ: искомая скорость должна быть равна 0,6 скоростей света
Очевидно, что для того чтобы эллипс превратился в круг необходимо равенство его главных осей. Речь идет о релятивистском сокращении длины стержня:
l=l0[$8730$](1-(v/c)^2),
где l0 - длина в системе наблюдателя, l - длина в движущейся системе, v-скорость движущейся системы, с - скорость света в вакууме
Тогда становится очевидно, что для того чтобы получился круг эллипс должен двигаться вдоль большей из главных осей.
Тогда получаем:
0,8*l0=l0[$8730$](1-(v/c)^2)
0,8=[$8730$](1-(v/c)^2)
0,64=1-(v/c)^2
(v/c)^2=0,36
v/c=0,6
v=0,6c
Ответ: искомая скорость должна быть равна 0,6 скоростей света
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